Bounce the car up and down, if the bushings are that bad you will hear them. Spray some lube on them and see if it quiets temporarily. If this loud squeaking is just from backing up, it is not the bushings but a bad wheel cylinder on a brake caliper could be the culprit. Check to see if 1 rotor is getting a lot more wear or grooving than the others. You said brakes were recently done, what did they replace? Pads and rotors both I hope.